No Arabic abstract
The possibility to detect circumbinary planets and to study stellar magnetic fields through binary stars has sparked an increase in the research activity in this area. In this paper we revisit the connection between stellar magnetic fields and the gravitational quadrupole moment $Q_{xx}$. We present three magnetohydrodynamical simulations of solar mass stars with rotation periods of 8.3, 1.2, and 0.8 days and perform a detailed analysis of the magnetic and density fields using a spherical harmonic decomposition. The extrema of $Q_{xx}$ are associated with changes of the magnetic field structure. This is evident in the simulation with a rotation period of 1.2 days. Its magnetic field has a much more complex behaviour than other models as the large-scale non-axisymmetric field dominates throughout the simulation and the axisymmetric component is predominantly hemispheric. This triggers variations in the density field that follow the magnetic field asymmetry with respect to the equator, changing the $zz$ component of the inertia tensor, and thus modulating $Q_{xx}$. The magnetic fields of the other two runs are less variable in time and more symmetric with respect to the equator such that there are no large variations in the density, therefore only small variations in $Q_{xx}$ are seen. If interpreted via the classical Applegate mechanism (tidal locking), the quadrupole moment variations obtained in the simulations are about two orders of magnitude below the observed values. However, if no tidal locking is assumed, our results are compatible with the observed eclipsing time variations.
Stellar winds are an integral part of the underlying dynamo, the motor of stellar activity. The wind controls the stars angular momentum loss, which depends on the magnetic field geometry which varies significantly in time and latitude. Here we study basic properties of a self-consistent model that includes simple representations of both the global stellar dynamo in a spherical shell and the exterior in which the wind accelerates and becomes supersonic. We numerically solve an axisymmetric mean-field model for the induction, momentum, and continuity equations using an isothermal equation of state. The model allows for the simultaneous generation of a mean magnetic field and the development of a Parker wind. The resulting flow is transonic at the critical point, which we arrange to be between the inner and outer radii of the model. The boundary conditions are assumed to be such that the magnetic field is antisymmetric about the equator, i.e., dipolar. At the solar rotation rate, the dynamo is oscillatory and of $alpha^2$ type. In most of the domain, the magnetic field corresponds to that of a split monopole. The magnetic energy flux is largest between the stellar surface and the critical point. The angular momentum flux is highly variable in time and can reach negative values, especially at midlatitudes. At rapid rotation of up to 50 times the solar value, most of the magnetic field is lost along the axis within the inner tangential cylinder of the model. The model reveals unexpected features that are not generally anticipated from models that are designed to reproduce the solar wind: highly variable angular momentum fluxes even from just an $alpha^2$ dynamo in the star. A major caveat of our isothermal models with a magnetic field produced by a dynamo is the difficulty to reach small enough plasma betas without the dynamo itself becoming unrealistically strong inside the star.
The variable magnetic field of the solar photosphere exhibits periodic reversals as a result of dynamo activity occurring within the solar interior. We decompose the surface field as observed by both the Wilcox Solar Observatory and the Michelson Doppler Imager into its harmonic constituents, and present the time evolution of the mode coefficients for the past three sunspot cycles. The interplay between the various modes is then interpreted from the perspective of general dynamo theory, where the coupling between the primary and secondary families of modes is found to correlate with large-scale polarity reversals for many examples of cyclic dynamos. Mean-field dynamos based on the solar parameter regime are then used to explore how such couplings may result in the various long-term trends in the surface magnetic field observed to occur in the solar case.
Solar magnetic activity shows both smooth secular changes, such as the Grand Modern Maximum, and quite abrupt drops that are denoted as Grand Minima. Direct numerical simulations (DNS) of convection driven dynamos offer one way of examining the mechanisms behind these events. In this work, we analyze a solution of a solar-like DNS that has been evolved for roughly 80 magnetic cycles of 4.9 years, during which epochs of irregular behavior are detected. The emphasis of our analysis is to find physical causes for such behavior. The DNS employed is a semi-global (wedge) magnetoconvection model. For data analysis we use Ensemble Empirical Mode Decomposition (EEMD) and phase dispersion ($D^2$) methods. A special property of the DNS is the existence of multiple dynamo modes at different depths and latitudes. The dominant mode is solar-like. This mode is accompanied by a higher frequency mode near the surface and a low-frequency mode in the bottom of the convection zone. The overall behavior of the dynamo solution is very complex exhibiting variable cycle lengths, epochs of disturbed and even ceased surface activity, and strong short-term hemispherical asymmetries. Surprisingly, the most prominent suppressed surface activity epoch is actually a global magnetic energy maximum. We interpret the overall irregular behavior to be due to the interplay of the different dynamo modes showing different equatorial symmetries, especially the smoother part of the irregular variations being related to the variations of the mode strengths, evolving with different and variable cycle lengths. The abrupt low activity epoch in the dominant dynamo mode near the surface is related to a strong maximum of the bottom toroidal field strength, which causes abrupt disturbances especially in the differential rotation profile via the suppression of the Reynolds stresses.
The surprising thinness of the solar tachocline is still not understood with certainty today. Among the numerous possible scenarios suggested to explain its radial confinement, one hypothesis is based on Maxwell stresses that are exerted by the cyclic dynamo magnetic field of the Sun penetrating over a skin depth below the turbulent convection zone. Our goal is to assess under which conditions (turbulence level in the tachocline, strength of the dynamo-generated field, spreading mechanism) this scenario can be realized in the solar tachocline. We develop a simplified 1D model of the upper tachocline under the influence of an oscillating magnetic field imposed from above. The turbulent transport is parametrized with enhanced turbulent diffusion (or anti-diffusion) coefficients. Two main processes that thicken the tachocline are considered; either turbulent viscous spreading or radiative spreading. An extensive parameter study is carried out to establish the physical parameter regimes under which magnetic confinement of the tachocline that is due to a surface dynamo field can be realized. We have explored a large range of magnetic field amplitudes, viscosities, ohmic diffusivities and thermal diffusivities. We find that, for large but still realistic magnetic field strengths, the differential rotation can be suppressed in the upper radiative zone (and hence the tachocline confined) if weak turbulence is present (with an enhanced ohmic diffusivity of $eta > 10^{7-8} , cm^2/s$), even in the presence of radiative spreading. Our results show that a dynamo magnetic field can, in the presence of weak turbulence, prevent the inward burrowing of a tachocline subject to viscous diffusion or radiative spreading.
YY Gem is a short-period eclipsing binary system containing two nearly identical, rapidly rotating, very active early-M dwarfs. This binary represents an important benchmark system for calibrating empirical relations between fundamental properties of low-mass stars and for testing theories of interior structure and evolution of these objects. Both components of YY Gem exhibit inflated radii, which has been attributed to poorly understood magnetic activity effects. Despite a long history of magnetic activity studies of this system no direct magnetic field measurements have been made for it. Here we present a comprehensive characterisation of the surface magnetic field in both components of YY Gem. We reconstructed the global field topologies with the help of a tomographic inversion technique applied to high-resolution spectropolarimetric data. This analysis revealed moderately complex global fields with a typical strength of 200-300 G and anti-aligned dipolar components. A complementary Zeeman intensification analysis of the disentangled intensity spectra showed that the total mean field strength reaches 3.2-3.4 kG in both components of YY Gem. We used these results together with other recent magnetic field measurements of M dwarfs to investigate the relation between the global and small-scale fields in these stars. We also assessed predictions of competing magnetoconvection interior structure models developed for YY Gem, finding that only one of them anticipated the surface field strength compatible with our observations. Results of our star spot mapping of YY Gem do not support the alternative family of theoretical stellar models which attempts to explain the radii inflation by postulating a large spot filling factor.